Black holes

Black holes don’t “suck” in matter any more than a star of the same mass. Orbits of particles are the same. In fact, black holes are less likely to swallow a particle, because it’s smaller, and most particles fly right past the black hole. You need a head-on collision to get destroyed, and for black holes, being very small, that’s rare:

Rotating (Kerr) black hole. Particle falls, is frame-dragged, orbits an infinite number of times before reaching the event horizon:

At the event horizon, light cones tip over, so an outside cannot say: “the falling thing has crossed the horizon”:

At the event horizon, clocks slow to zero. As with the Shapiro delay, you could bounce just outside the event horizon, and reappear after a trillion years:

Slow light

For the same measured distance, light takes different time to bounce and return. This Shapiro delay can be arbitrarily large when bouncing close to the event horizon of a black hole. Taylor and Wheeler refer to this as “slow light”:

Measuring the local speed of light always gives c, because your measurement equipment slows along with light.

Wormholes

Travel the quick way, through a wormhole:

Build a worm hole by connecting two “mouths” in the embedding dimension:

Morris-Thorne wormhole. Step into one mouth, step out the other (along yellow rods):

The two wormhole mouths can be attached at different times:

Same skewed attachment with the t coordinate visualized. You can the make a time machine (more here).

Cosmology

The universe looks the same from everywhere, even when it’s closed:

A closed universe is not infinite. Go straight, and you loop back to where you started, just like on planet Earth’s surface.

A closed universe is not infinite. It could be like the surface of the Earth, closing back on itself (in an embedding dimension), or it could be a hot plate (see Feynman’s lecture), where spacetime distorts just so that it behaves like a spherical surface. You get different boundary conditions for a path that hits the edge head on:

In an open (infinite) universe, turn the curvature up and down:

With expansion, space is added between galaxies that sit still. Cosmic time is measured “at rest” and runs the fastest. A moving clock (for example one at fixed distance during expansion) shows less time:

With expansion, matter and radiation is diluted. Dark-energy density stays the same:

The expansion rate of the universe is measured in [1/s], not [m/s]. It’s not a speed. So please don’t say that “it’s expanding faster than light.” However, the distance [m] between two galaxies changes with time [m/s], so you can call this a recession speed. The further apart, the higher the recession speed. You can always find two points receding faster than light, even when expansion is slow:

During 13 billion years, a galaxy can recede by much more than 13 billion light-years, because of expansion. A photon emitted by the receding galaxy may initially be “expanded away,” then eventually catch up and reach us.

Special Relativity

The three effects at high speed: length contraction, time dilation, desynchronization:

Synchronize clocks while moving: Method 1. Flash light halfway between clocks, reset clocks to zero when they detect the flash. Fails on moving ship). because flash takes longer to catch up to front clock:

Conspiracy of nature: Moving, contracted ship measures at-rest, long ship to be contracted:

Conspiracy of nature: Moving ship has slow clocks, but measures at-rest fast clocks to be slow! Why? Because moving clocks are desynchronized:

Paradoxes evaporate with you remember that it’s all about measurements, by an observer that may be moving, not about some global, external POV:

Conspiracy of nature: When you and your meter stick both contract, you cannot tell (locally):

Conspiracy of nature: When you and your clocks run in slow motion, you cannot tell (locally). Also note tilted rod (clock desynchronization):

For a spinning ring, you get time dilation. For length contraction, it’s the instantaneous velocity that matters. The spokes don’t get shorter, but the yellow rods do, so you get gaps:

For the spinning ring, you cannot synchronize clocks all the way around (blue light flashes propagate):

Breathers (sine-Gordon)

A non-linear string can “trap” the energy of a disturbance. Below, the top string oscillates between kinetic and potential energy, in one location, like a particle at rest. (The boring linear string, bottom: waves rush off at the speed of the medium, c):

Sine-Gordon breathers, like particles, obey Special Relativity: they contract, the oscillations dilate in time, and the front lags behind the rear. Also, the total energy, E = T+U of the non-linear string, increases with a -factor:

Sine-Gordon breathers, like particles, obey General Relativity in one respect: they accelerates toward where c (the speed of the medium) is smaller:

Particles

Binding energies: the more tightly bound, the more energy needed to remove. For quarks, so much energy is input that new quarks are created, bonding with the remnants: